Application of derivatives Questions and Answers

and an equation for the plane which contains the point 1 2 3 and which is parallel ane 3x y2z 15

Use a Venn Diagram Let P Z 0 42 P Y 0 33 and P Z UY 0 57 Find each a P Z nY b P Z UY c P Z UY d P ZnY d x a 24 b 18 C 15 d 43 Type integers or decimals a P Z n Y 0 18 Type an integer or a decimal

Let P Z 0 43 P Y 0 42 and P ZnY 0 18 Use a Venn diagram to find a P Z nY b P Z UY c P Z UY and d P ZNY a P Z nY 33 Type an integer or a decimal b P Z UY 82 Type an integer or a decimal c P Z UY 75 Type an integer or a decimal d P ZnY Type an integer or a decimal TH

Sketch the graphs off and g in the same coordinate plane Include two full periods f x sin x g x 3 sin x O y 2 SANAA 2x 2 3x 2 27 3 A 2 X 21 5 4 3 AA 2 2 2 3 4 5 X O 3x 2 5 4 3 ah www 2 1 2x 2 y 3x 2 2m X

f x x 1 Consider the portion of the curve where y 1 4 Find the surface area of the surface generated by revolving the graph of f x around the Y axis Round your answer to the nearest whole number

purchased kitchen A restaurant equipment on January 1 2017 On January 1 2019 the value of the equipment was 17 550 The value after that date was modeled as follows V t 17 550e 0 171t a

Find A the area of the region under the curve y 7 3x and above the x axis

Consider the quadratic function x x 6x 8 PART A Determine the vertex and rewrite the function in vertex form 3 marks PART B Determine the y intercept 1 mark PART C Factor the expression by inspection trial and error 1 mark Use the quadratic formula to verify your answer 1 mark Using this what are the X intercepts 1 mark PART D What is the domain and range 2 marks PART E Using all points and information given in this problem sketch the graph 2 marks

Write the equation of a sine or cosine function to describe the graph 34 2 15 10

Cose sece csc0 It cote 1 Cot 0 1 1 Cot 8 1 2 sin 0

Use the graph of the function f Is there a local maximum at 10 If yes what is it Select the correct choice below and if necessary fill in the answer box within your choice OA Yes there is a local maximum at 10 and it is Type an integer or a fraction OB There is no local maximum at 10 10 9 13 0 7 0 18 15 1 0 4 9 15 1 4 3 0 18

A radio tower has a 42 foot shadow cast by the sun If the angle from the tip of the shadow to the top of the tower is 84 what is the height of the radio tower Round your solution to four decimal places

Find the average rate of change of the function over the given interval R 0 50 1 3 16 AR Simplifu new

a Find the average value of f x 25 2 on the interval 0 3 Answer b Find a value c in the interval 0 3 such that f c is equal to the average value

Find a function f and a positive number a such that f x 19 dt f t 4 2 dt 3x 3

Find all real solutions of the equation by completing the square Enter your answers as a comma separated list x 2 4x 1 0 X

Calculate the derivative fint cos 2 de 1 de

Given f x At what value of a does the local max of f x occur t 36 1 cos t dt

DP Math 7 Find the coordinates on the function f x x 1 closest to the point 3 1

The graph below is the function f x 5 4 3 2 1 3 2 2 N 3 4 23 Select all statements below that you agree with Note You may be checking more than one box No partial credit Of 2 is defined lim f x exists x 2 Olim f x f 2 The function is continuous at x 2

Graph the function Find the intervals on which the function is increasing or decreasing Find any 10x x 1 M 7 f x 0 6x 9 x2 for 3 sx 3 relative extrema

Find the exact extreme values of the function z f x y 35 x 12 y 100 subject to the following constraints begin array I y geq 0 y leq 36 x 2 end array Complete the following begin array f min text at x y quad f max text at x y text end array

Find the exact value of each expression a tan arctan 7 b arcsin sin 5 4

8 A curve C is defined implicitly by the equation x3 y 6xy find a y in terms of x and y b The equation of the tangent to C at the point 3 3 c The coordinates of the points on C where the tangent line is horizontal 3 3

DP Math AAH 7 Find the coordinates on the function f x x 1 closest to the point 3 1

A A B f 2 f 1 2 1 QIn parts A C find the indicated quantity for y f x 6 x 3 f 1 h f 1 b 5

valuate the integral Use C for the constant of integration 3 e 18 dr

ifferentiate the function f z e z 4 z

Differentiate the function f x 6x 9x e

udy determined that 3 of children under 18 years of age live with their father only Find st 2 persons selected at random from 15 children under 18 years of age lived with their f probability that at most 2 children live with their father only is 0096 not round until the final answer Then round to the nearest thousandth as needed

cording to a report from a particular university 46 of female undergraduat t none of the female undergraduates have taken on debt if 8 female underg at probability should be found A P 8 female undergraduates take on debt B P 0 female undergraduates take on debt C P 2 female undergraduates take on debt D P 1 female undergraduate takes on debt probability that none of the female undergraduates take on debt is pe an integer or decimal rounded to three decimal places as needed

You re flying from Joint Base Lewis McChord JBLM to an undisclosed location 293 km south and 215 km east Mt Rainier is located approximately 56 km east and 40 km south of JBLM If you are flying at a constant speed of 800 km hr how long after you depart JBLM will you be the closest to Mt Rainier minutes

certain state pickup trucks account for 28 of the state s registered ve ted at random what is the expected number of pickup trucks expected number of pickup trucks is

Factor a sec 0 1 C ter c cot x cot x cos x Acive b 4 tan 0 tan 0 3 d csc x cotx 3

Let 0 c 1 and let f 0 f 0 1 R f x if x c 0 if x c Prove directly from the definition of Riemann integrability that f is Riemann integrable on 0 1 1 and that s Hint Let 8 0 and let P be a partition of 0 1 of mesh less than 8 Show that 0 U f P 28 by distinguishing the cases that c is a partition point of P and that c is not a partition point of P

function f that satisfies the following lim x rightarrow infty f x 2 lim x rightarrow infty f x 2 lim x rightarrow 1 f x infty lim x rightarrow 1 f x infty lim x rightarrow 3 f x infty lim x rightarrow 3 f x infty

with 7 d A midpoint approximation subintervals over 0 2 What is the left endpoint approximation s 6 for f x x 3 over 2 4 a 45 44 b 51 00 c 60 00 d 64 11

2 9 2 dx where g x has the values given in the following table x 0 0 5 1 1 5 2 2 5 3 g x 0 5 2 2 3 9 4 8 5 4 7 7 99 To solve this exercise 1 Use integration by parts to simplify the integral 2 Estimate the remaining integral using a left Riemann sum Select a blank to input an answer

Select all statements that are can be true about the polynomial function whose graph is given in the figure below 2 0 00 00 0 1 y 0 1 2 If this is a third degree polynomial the constant term of this polynomial is negative X This function is continuous and differentiable between x 2 and x 2 The degree of this polynomial can be less than three This function is neither continuous nor differentiable between x 2 and x 2 The degree of this polynomial can be more than or equal to three If this is a third degree polynomial the constant term of this polynomial is positive This function is continuous but not differentiable between x 2 and x 2

Write the equation of g x the transformed function with a parent function of f x log x graphed below g x will be in the form g x a log2 xh k Note from the graph that the point 0 2 is visible and you may also use the point 1 1 4 32 ny O

23 You just bought a Japanese car with a 2 6 liter engine How many gallons is this 24 You have a fish aquarium that hold 825 in of water How many milliliters of water is in the tank 1 gal 231 in

21 235 5 inches miles 22 Suppose you found a gold coin in your backyard and wanted to determine its value Y knew that gold was selling for 323 12 per ounce You bring it to the lab but the lab scale only give you a mass in grams What is the value of the coin if it weighs 8 7739 grams

QUESTION 8 Use cross multiplication to solve for the unknown in each of the followi 6 5 2 5 X 11 2 QUESTION 9 23 Use cross multiplication to solve for the unknown in each of the following proportions 2 30 11 Ni roportions X

A mass is placed on a smooth inclined plane with an angle of 30 to the horizontal If the inclined plane is 5 0 m long how long does it take for the mass to reach the bottom of the inclined plane after it is released from rest O 1 4 s O 1 0 s O 1 1 s O 1 3 s

An object sits on a frictionless surface A 16 N force is applied to the object and it accelerates at 4 0 m s What is the mass of the object O 32 kg O 4 0 kg 8 0 kg O 78 N

distance d from the point 6 9 7 to the plane x 2y 5z 33 d

uate the factorial 91 Type a whole number

3 Given the following matrix 2 1 1 642 4 4 4 8 1 1 a Determine the rank of A b Based on the rank of A A is the rows of the matrix linearly independent what about the columns explain your answer

Points U of nd the expected payback for a game in which you bet 6 on any number from 0 et 500 e expected payback is tound to the nearest cent as needed

q 4 1 What is the binary value of 37 dec